## Abstract

Previously a theory has been presented which extends the geometrical structure of a real four-dimensional space-time via a field of orthonormal tetrads with an enlarged transformation group. This new transformation group, called the conservation group, contains the group of diffeomorphisms as a proper subgroup. The fundamental geometric object of the new geometry, called the curvature vector, is used to form a scalar Lagrangian density from which field equations for the free field are obtained. These field equations are invariant under the conservation group. The theory is further extended by development of a suitable Lagrangian for a field with sources. Spherically symmetric solutions for both the free field and the field with sources are given. A stellar model and an external, free-field model are developed. The theory implies that the external stress-energy tensor has non-compact support and hence may give the geometrical foundation for dark matter. The resulting models are compared to the internal and external Schwarzschild models. The theory may explain the Pioneer anomaly and the corona heating problem.

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## Metadata

- Subject
Physics & Astronomy

- Date submitted
18 July 2022

- Keywords
- Additional information
*Author Biography:*Mathematics Department